hey guys. i know with being said that over-training is like not training at all because of the major strain you put on your muscles but i have a hypothesis and was wondering if you could give me some input on it and clear it up for me. so could you do three sets of push-ups (3 sets of 25 for example) then rest and do core or something for like 20 minutes, then go over to the bench and do three sets of a weight(3 sets of 8 reps) so you get your endurance and your strength/mass in all in one or is that overtraining?

There are a few types of overtraining so we should probably distinguish between a few.

The first, and in my mind the easiest trap to fall into, is not resting enough. Soreness is due to the microscopic tears in your muscle fibers that accompanies weight training. The purpose of rest is to let those tears heal bigger and stronger. If you work out your chest while still sore from the previous chest workout you are on a fast track to overtraining.

It seems like you are referring to overtraining as in massively overworking one part of your body and causing damage. This is definitely possible but personally I think it is much harder to do because you hit a point where fatigue and lactic acid prevent you from lifting anymore. If you push through the fatigue and continue lifting after your body has already asked you to stop then you can tear your muscles down too much.

...and my 2 cents is that those two exercises you mentioned are definitely not overtraining. I would personally do it without the long rest in between. just wait 3-4 minutes. If you want to get the most out of the strength portion I'd suggest doing bench first and the pushups last.